%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM427+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:40:29 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 59 ( 16 unt; 8 def)
% Number of atoms : 179 ( 33 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 195 ( 75 ~; 79 |; 27 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 43 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1,W2] :
( ( W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f32,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,plain,
! [W0,W1] :
( aInteger0(sdtasdt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f37,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f66,plain,
! [W0] :
( ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f67,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(NNF_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [W0] :
( ( ! [W1] :
( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f69,plain,
! [W0] :
( ( ! [W1] :
( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( sdtasdt0(W1,sK0_skl(W1,W0)) = W0
& aInteger0(sK0_skl(W1,W0))
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f68]) ).
fof(f74,plain,
! [X0,X1,X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| X1 = sz00
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f75,plain,
! [W0,W1,W2] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f76,plain,
! [W0,W1,W2] :
( ( ( ~ aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))
| sdteqdtlpzmzozddtrp0(W0,W1,W2) )
& ( aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(NNF_transformation,[status(thm)],[f75]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2)
| X2 = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f81,plain,
aInteger0(xa),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f82,plain,
aInteger0(xb),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f83,plain,
aInteger0(xq),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f84,plain,
xq != sz00,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f86,plain,
aInteger0(xn),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f88,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f89,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f91,plain,
! [X1,X2] :
( ~ aInteger0(X2)
| X1 = sz00
| ~ aInteger0(X1)
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(sdtasdt0(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f74]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| X0 = sz00
| ~ aInteger0(X0)
| aDivisorOf0(X0,sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f37]) ).
fof(f93,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xb) ),
inference(resolution,[status(thm)],[f78,f89]) ).
fof(f94,definition,
( sQ0_spl
<=> aInteger0(xb) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( sQ0_spl
| ~ aInteger0(xb) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ1_spl
<=> aInteger0(xa) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f99,plain,
( sQ1_spl
| ~ aInteger0(xa) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
( sQ2_spl
<=> aInteger0(xq) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( sQ2_spl
| ~ aInteger0(xq) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,definition,
( sQ3_spl
<=> xq = sz00 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ3_spl
| xq = sz00 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
( sQ4_spl
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( sQ4_spl
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( ~ sQ4_spl
| sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f93,f94,f97,f100,f103,f106]) ).
fof(f110,plain,
( sQ4_spl
| ~ aDivisorOf0(xq,sdtasdt0(xq,smndt0(xn))) ),
inference(forward_demodulation,[status(thm)],[f88,f108]) ).
fof(f135,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f83]) ).
fof(f136,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f142,plain,
( sQ4_spl
| ~ aInteger0(smndt0(xn))
| xq = sz00
| ~ aInteger0(xq) ),
inference(resolution,[status(thm)],[f110,f92]) ).
fof(f143,definition,
( sQ10_spl
<=> aInteger0(smndt0(xn)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( sQ10_spl
| ~ aInteger0(smndt0(xn)) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( sQ4_spl
| ~ sQ10_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f142,f100,f103,f143,f106]) ).
fof(f147,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f104,f84]) ).
fof(f148,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f149,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f81]) ).
fof(f150,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f82]) ).
fof(f152,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f155,plain,
( sQ10_spl
| ~ aInteger0(xn) ),
inference(resolution,[status(thm)],[f145,f33]) ).
fof(f156,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f86]) ).
fof(f157,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f158,plain,
$false,
inference(sat_refutation,[status(thm)],[f109,f136,f146,f148,f150,f152,f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM427+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:28:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.055677 seconds
% 0.13/0.43 % CPU time: 0.160909 seconds
% 0.13/0.43 % Total memory used: 102.384 MB
% 0.13/0.43 % Net memory used: 102.245 MB
%------------------------------------------------------------------------------